We review the use of emission lines for understanding galaxy evolution, focusing on excitation source, metallicity, ionization parameter, ISM pressure, and electron density. We discuss the physics, benefits, and caveats of emission line diagnostics, including the effects of theoretical model uncertainties, diffuse ionized gas, and sample selection bias. In anticipation of upcoming telescope facilities, we provide new self-consistent emission line diagnostic calibrations for complete spectral coverage from the UV to the IR. These diagnostics can be used in concert to understand how fundamental galaxy properties have changed across cosmic time. We conclude the following: The UV, optical, and IR contain complementary diagnostics that can probe the conditions within different nebular ionization zones. Accounting for complex density gradients and temperature profiles is critical for reliably estimating the fundamental properties of Hii regions and galaxies. Diffuse ionized gas can raise metallicity estimates, flatten metallicity gradients, and introduce scatter in ionization parameter measurements. New 3D emission line diagnostics successfully separate the contributions from star formation, AGN, and shocks using integral field spectroscopy.We summarize with a discussion of the challenges and major opportunities for emission line diagnostics in the coming years.